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3 sie 2024 · The converse of the conditional statement is “If Q then P.”. The contrapositive of the conditional statement is “If not Q then not P.”. The inverse of the conditional statement is “If not P then not Q.”. We will see how these statements work with an example.
The inverse of the conditional \(p \rightarrow q\) is \(\neg p \rightarrow \neg q\text{.}\) The contrapositive of this new conditional is \(\neg \neg q \rightarrow \neg \neg p\text{,}\) which is equivalent to \(q \rightarrow p\) by double negation.
28 lis 2020 · The contrapositive is logically equivalent to the original statement. The converse and inverse may or may not be true. When the original statement and converse are both true then the statement is a biconditional statement.
The contrapositive is "If a polygon does not have four sides, then it is not a quadrilateral." This follows logically, and as a rule, contrapositives share the truth value of their conditional. The inverse is "If a polygon is not a quadrilateral, then it does not have four sides.
The converse, inverse, and contrapositive are variations of the conditional statement, p → q. The converse is if. q then. p, and it is formed by interchanging the hypothesis and the conclusion. The converse is logically equivalent to the inverse.
11 lis 2022 · The contrapositive of an implication is the converse of its inverse (or the inverse of its converse, which amounts to the same thing). That is, \[\text{ the contrapositive of } A\Rightarrow B\text{ is the implication }\lnot B\Rightarrow\lnot A\]
Understand the fundamental rules for rewriting or converting a conditional statement into its Converse, Inverse & Contrapositive. Study the truth tables of conditional statement to its converse, inverse and contrapositive.
